Waveguide modulation is important in the areas of optical communication and high-speed signal processing. Switching and modulation can be accomplished in nonlinear optical waveguides by modifying the propagation constant of a guided mode through the application of an electric field via the linear electrooptic effect. The applied electric field provides a change in refractive index and can result in phase and/or intensity modulation. Voltage is applied to two electrodes placed over or alongside the waveguide. The vertical electric field is employed when one electrode is placed directly over the waveguide, while the horizontal electric field is used when the electrodes are placed on either side of the waveguide. The applied electric field is not uniform and peaks sharply near the electrode edge. See "Optical Electrode Design for Integrated Optics Modulators", by D. Marcuse, IEEE Journal of Quantum Electronics, Vol. QE-18, 393 (1982). The uniformity of the electric field can be improved by moving the two electrodes sufficiently far apart. However, this requirement necessitates a high drive voltage because the magnitude of the field is approximately equal to V/G where G is the electrode gap.
A variety of parametric devices has been developed for efficient frequency conversion. Parametric processes in nonlinear optical materials require phase matching of the interacting optical modes to achieve very efficient nonlinear optical interactions. Periodic inversion of the ferroelectric domain structure of LiNbO.sub.3 and LiTaO.sub.3 has been used for quasi-phase matching, thus permitting generation of blue light in a guided mode of the waveguide. Yamada et al formed a periodic domain structure in LiNbO.sub.3 bulk crystals by applying an external electric field. See "First-order Quasi-phase Matched LiNbO.sub.3 Waveguide Periodically Poled by Applying an External Field for Efficient Blue Second-harmonic Generation", by M. Yamada, N. Nada, M. Saitoh, and K. Watanabe, Appl. Phys. Lett. 62, 435 (1993). The field V/T must be greater than the electric coercive force with a value of 20 kV/mm for LiNbO.sub.3, where T is the bulk crystal thickness. For instance, voltage level above 4 kV is needed for domain inversion in 200 .mu.m-thick LiNbO.sub.3 bulk crystals. For thin films grown on foreign substrates, the electric field is approximately equal to .epsilon..sub.2 V/.epsilon..sub.1 T where .epsilon..sub.1 and .epsilon..sub.2 are the respective dielectric constants of the film and substrate, and T is the total thickness of the sample. Using the known values of the dielectric constants listed, one can find that voltage with a magnitude of 10.7 kV is required for domain inversion in a c-oriented LiNbO.sub.3 film grown on a sapphire substrate with a total thickness of 200 .mu.m. Since higher voltage is required, achieving domain inversion by an electric field is more difficult in thin films than in bulk. Although one can further mill the substrate to reduce the required voltage level, a tradeoff exists between the voltage required for domain inversion and the minimum thickness required for mechanical rigidity.